A 225-kg object and a 525-kg object are separated by 3.30 m.
(a) Find the magnitude of the net gravitational force exerted by these objects on a 38.0-kg object placed midway between them.
(b)At what position (other than an infinitely remote one) can
the 38.0-kg object be placed so as to experience a net force of
zero from the other two objects?
______________ m from the 525 kg mass toward the 225 kg mass
Part A)
F = Gmm/r2 - Gmm/r2
F = (6.67 X 10-11)(525)(38)/(1.65)2 - (6.67 X 10-11)(225)(38)/(1.65)2
F = 2.79 X 10-7 N (.000000279 N)
Part B)
In this case, Gmm/r2 will need to equal each other and G and the 38 kg mass will cancel leaving
m/r2 = m/r2
225/x2 = 525/(3.3 - x)2
Cross multiply
225(3.3 - x)2 = 525x2
2450.25 - 1485x + 225x2 = 525x2
In standard form, that is 300x2 + 1485x - 2450.25 = 0
Find the roots using the quadratic equation
The roots are...1.30 and -6.26
The negative root can be eliminated since that distance is outside the masses
Thus the distance is 1.30 m from the 225 kg mass
Thus 3.3 = 1.3 = 2.0 m from the 525 kg mass
(225 kg) ------1.15 m------ (38 kg) ------1.15 m------ (525 kg)
(a) For the Left Half:
(225 kg) ------1.15 m------ (38 kg)
F = G M m / d^2
= 4.312E-7 N
For the Right Half:
(38 kg) --6----1.15 m------ (525 kg)
F = G N m / d^2
=1.00617E-6 N
The difference, or net force, is 5.74973E-7 N.
b).
(225 kg) ------3.3-x m------ (38 kg) ------x m------ (525 kg)
F-f =0
F - force exerted by 225 on 38kg
and f - force exerted by 525 on 38kg
G *38*525 / x^2 = G * 38*225 / (3.3-x)^2
(3.3-x)^2 / x^2 = 225 /525
(10.89 +x^2 -6.6x ) *525 = 225*x^2
5717.25 + 525x^2 -3465x = 225x^2
300x^2 -3465x + 5717.25 = 0
x1=1.99437m from 525kg towards 225kg
Grav force = Gm1m2/r2
So net force = F1-F2
=4.9* 10-7 -2.1 * 10-7 = 2.8 * 10-7 N
B) F1= F2
525/R2 = 225/ (3.3-R) 2
R= 2m approx from 525 kg
A 225-kg object and a 525-kg object are separated by 3.30 m. (a) Find the magnitude...
Objects with masses of 225 kg and a 525 kg are separated by 0.500 m. (a)Find the net gravitational force exerted by these objects on a 70.0 kg object placed midway between them. magnitude __??____ direction: toward the 225 kg mass toward the 525 kg mass The magnitude is zero. (b) At what position (other than infinitely remote ones) can the 70.0 kg object be placed so as to experience a net force of zero? __??____ m from the 525...
Objects with masses of 225 kg and a 525 kg are separated by 0.500 m. (a) Find the net gravitational force exerted by these objects on a 56.0-kg object placed midway between them. magnitude direction toward the 525-kg mass (b) At what position (other than infinitely remote ones) can the 56.0-kg object be placed so as to experience a net force of zero? Did you accidentally divide or take the inverse in your calculation? m from the 525-kg mass The...
A 280-kg object and a 580-kg object are separated by 3.40 m. Find the magnitude of the net gravitational force exerted by these objects on a 65.0-kg object placed midway between them. Draw a picture of the three objects, including the forces exerted on the third. N At what position (other than an infinitely remote one) can the 65.0-kg object be placed so as to experience a net force of zero from the other two objects? m from the 580...
A 280-kg object and a 580-kg object are separated by 3.50 m. (a) Find the magnitude of the net gravitational force exerted by these objects on a 33.0-kg object placed midway between them. _________N (b) At what position (other than an infinitely remote one) can the 33.0-kg object be placed so as to experience a net force of zero from the other two objects? _____________m from the 580 kg mass toward the 280 kg mass
A 280-kg object and a 580-kg object are separated by 3.40 m. (a) Find the magnitude of the net gravitational force exerted by these objects on a 58.0-kg object placed midway between them. Incorrect: Your answer is incorrect. Draw a picture of the three objects, including the forces exerted on the third. N (b) At what position (other than an infinitely remote one) can the 58.0-kg object be placed so as to experience a net force of zero from the...
Objects with masses of 130 kg and a 430 kg are separated by 0.360 m. (a) Find the net gravitational force exerted by these objects on a 40.0-kg object placed midway between them. magnitude ____ N What is the Direction: a.toward the 130kg mass b. toward the 430kg mass c. the magnitude is zero (b) At what position (other than infinitely remote ones) can the 40.0-kg object be placed so as to experience a net force of zero? ________ m...
Help me solve this physics problem please. A 140-kg object and a 440-kg object are separated by 4.60 m. Find the magnitude of the net gravitational force exerted by these objects on a 67.0-kg object placed midway between them. Draw a picture of the three objects, including the forces exerted on the third. N (b) At what position (other than an infinitely remote one) can the 67.0-kg object be placed so as to experience a net force of zero from...
Objects with masses of 140 kg and a 440 kg are separated by 0.330 m. (a) Find the net gravitational force exerted by these objects on a 39.0-kg object placed midway between them. magnitude N (b) At what position (other than infinitely remote ones) can the 39.0-kg object be placed so as to experience a net force of zero? m from the 440-kg mass
Objects with masses of 205 kg and a 505 kg are separated by 0.330 m. (a) Find the net gravitational force exerted by these objects on a 46.0 kg object placed midway between them. magnitude direction -Select- N (b) At what position (other than infinitely remote ones) can the 46.0 kg object be placed so as to experience a net force of zero? m from the 505 kg mass
Objects with masses of 145 kg and a 445 kg are separated by 0.300 m. (a) Find the net gravitational force exerted by these objects on a 36.0-kg object placed midway between them. magnitude N direction (b) At what position (other than infinitely remote ones) can the 36.0-kg object be placed so as to experience a net force of zero? m from the 445-kg mass